The port-Hamiltonian concept is a powerful way to bring theory nearer physics, and suggest new computational approaches.
SA-amenability is a powerful concept in another way, making possible, or cheap to implement, numerical methods that without it are impossible or expensive.
Our contribution is to show that a particular mix of—mostly well known—ingredients gives a DAE that is both port-Hamiltonian and SA-amenable.
That it has index \(\le 1\)  was an unexpected bonus, which we suspect comes from obeying the pH injunction that the Hamiltonian be an algebraic function of the state variables.
Writing Kirchhoff's laws in terms of the \(F\)  matrix goes back at least to [1]}, [2]}, where also the zero blocks of \(F\)  are exploited though less transparently than here.
The existence of a normal tree is shown in [2]}.
Our main proof is a distillation of that in [4]} that the BOM circuit model's DAE is SA-amenable.
However, the BOM DAE is not pH and can have index 2.
Applying pH theory to electrical circuits is a topic of current research, see e.g. [5]}, [6]}.
In [5]}, selection of a ground node—not needed by CpH—plays a crucial role in defining the Dirac structure; and there is no discussion of the DAE index.
The aim of [6]} is to put the MNA equations in port-Hamiltonian form; this can lead to a DAE of index 2.
Neither work discusses SA-amenability.
To the best of our knowledge the CpH method construction, and SA-amenability and related proofs, are new.
So also appears to be our proof of Theorem REF , and the resulting direct counts of the number of linearly independent \({\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {V}}}\) -cycles (including \({\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}\) -cycles) \(n_{\hspace{0.2pt}\texttt {C}}=n_{\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}-r_{{\hspace{0.2pt}{\hspace{0.2pt}\texttt {V}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}} + r_{\hspace{0.2pt}{\hspace{0.2pt}\texttt {V}}}\) , and similarly of \({\hspace{0.2pt}{\hspace{0.2pt}\texttt {L}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {I}}}\) -cutsets \(n_{\hspace{0.2pt}\texttt {l}}=r_{{\hspace{0.2pt}{\hspace{0.2pt}\texttt {V}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {D}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {L}}}} - r_{{\hspace{0.2pt}{\hspace{0.2pt}\texttt {V}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {D}}}}\) .
Our CICs method in §REF  is new, but related to one in [9]}.
Our method is easy to automate: as said in §REF , from a [basicstyle=]CpH object representing a circuit we generate code simulating that circuit, in the form of a [basicstyle=]daefcn function accepted by an index-1 solver such as [basicstyle=]ode15i.
Other advantages of being SA-amenable is the systematic reduction to an ODE Subsection REF , the easy eigenvalue analyis for LTI systems Subsection REF , or the use of Mattsson-Söderlind dummy derivatives [10]}.
